For any bounded smooth domain Omega subset of R-3 (or Omega = R-3), we establish the global existence of a weak solution (u, d) : Omega x [0, +infinity) -> R-3 x S-2 of the initial boundary value (or the Cauchy) problem of the simplified Ericksen-Leslie system (1.1) modeling the hydrodynamic flow of nematic liquid crystals for any initial and boundary (or Cauchy) data (u(0), d(0)) is an element of H x H-1 (Omega, S-2), with d(0) (Omega) subset of S-+(2) (the upper hemisphere). Furthermore, (u, d) satisfies the global energy inequality (1.4). (C) 2016 Wiley Periodicals, Inc.
展开▼
机译：对于R-3的任何有界光滑域Omega子集（或Omega = R-3），我们建立了弱解的整体存在性（u，d）：Omega x [0，+无穷大]-> R-3 x S -简化的Ericksen-Leslie系统（1.1）的初始边界值（或Cauchy）问题的-2，用于建模向列液晶的流体动力学流，以获取任何初始和边界（或Cauchy）数据（u（0），d（0 ））是H x H-1（Omega，S-2）的元素，其中d（0）（Omega）是S-+（2）（上半球）的子集。此外，（u，d）满足全球能源不平等（1.4）。 （C）2016威利期刊公司
展开▼
